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The stabilization of expansive soils is crucial for the construction projects to mitigate swelling, shrinkage, and bearing capacity issues. This study investigates the synergistic effects of cement and clinoptilolite zeolite on stabilizing high-plasticity clay (CH) soil from Kano State, Nigeria. A total of 30 admixture combinations—cement (0–8%) and zeolite (0–15%)—were tested via standardized laboratory methods to evaluate their free swell index (FSI), swell percentage, swell pressure, shrinkage, and California Bearing Ratio (CBR). Principal component (Lasso) “least absolute shrinkage and selection operator” regression modeled interactions between admixtures and soil properties. The key results include the following: (1) 6% cement + 12% zeolite reduced the FSI by 60% (45 → 18); (2) 8% cement + 15% zeolite decreased the swell percentage by 47.8% (22.5% → 11.75%); (3) 6% cement + 12% zeolite lowered swell pressure by 54.2% (240 kPa → 110 kPa); (4) 8% cement + 12% zeolite reduced shrinkage by 50% (5.6% → 2.8%); and (5) 6% cement + 9% zeolite achieved an unsoaked CBR of 80.01% and soaked CBR of 72.79% (resilience ratio: 0.8010). PCLR models explained 93.5% (unsoaked) and 75.0% (soaked) of the CBR variance, highlighting how zeolite’s mediation analysis indicates that zeolite improves the bearing capacity mainly by reducing the free swell index (path coefficient = −0.91429, p < 0.0001), while conditional process modeling provided greater explanatory power (R² = 0.745) compared to moderation-only analysis (R² = 0.618). This study demonstrates that zeolite–cement blends optimize strength and resilience in expansive soils, with implications for sustainable infrastructure in arid and semi-arid regions. Full article